arrays, vectors , and matrices thursday 14th 2010

Arrays, Vectors , and Matrices Thursday 14th 2010

Thursday, October 14, 2010

Types of Arrays

Class/Type Construction and Size query Remarks

array

Double[] x = new Double[2];x[0] = 5.0;x[1] = 4.3;int size = x.length;

arrays cannot be extended once they are defined, these are rather dumb containers, but fast to access.

ArrayList

ArrayList x = new ArrayList();x.add(object1);x.add(object2);int size = x.size();

Elements in ArrayList need to be instances of classes, for example Double object1 = new Double(2.0)

Vector

Vector x = new Vector();x.add(object1);x.add(object2);int size = x.size();

Vector is a synonym of ArrayList and is phasing out.


Looping over Arrays

// x is an ArrayListDouble sum = new Double(0.0);Iterator xit = x.iterator();while (xit.hasNext()) { sum += (Double) xit.next();}

// x is and ArrayListDouble sum = new Double(0.0);int i;for(i=0; i < x.size();i++){ sum += (Double) x.get();}

// x is an ArrayListDouble sum = new Double(0.0);for(Object element : x){ sum += (Double) element;}

// x is a Double[] arrayDouble sum = new Double(0.0);int i;for(i=0; i < x.size();i++){ sum += (Double) x.get();}

// x is a Double[] arrayDouble sum = new Double(0.0);for(Double element : x){ sum += element;}

No iterator for array

for for

foreach

foreach

foreachforeach

while


Better use of ArrayList

ArrayList x = new ArrayList();Double value = new Double(5.0);x.add(value);

ArrayList evolved in recent Java version to use a Template in its initialization.We used simply

This is unsafe because we should make clear that we deal with Doubleand we can use a template mechanism:

ArrayList x = new ArrayList<Double>();Double value = new Double(5.0);x.add(value);

In the textbook you will see this often in the general form as ArrayList<T>, where Tis a Type, like Double, Int, or Long etc.


IteratorsTechnically, all indicators into an array are iterators, a device that helps us to orderly accessthe elements of an array.

In Java Iterator are more narrowly defined as a tool that can access a container class, for example an ArrayList (but there are many others: List, Vector, Hash, ...), in an orderly fashion, for example from the first to the last, even when the container class does not really allow standard indexing (like a hash). A container class MUST define a method iterator() that supplies the iterator.

Iterators come in two flavors: Iterator (very general but can only go in one direction), and ListIterator, that can go back and forth in the container and also can manipulate its content.

// x is an ArrayListDouble sum = new Double(0.0);Iterator<Double> xit = x.iterator();while (xit.hasNext()) { sum += (Double) xit.next();}

// x is an ArrayListDouble sum = new Double(0.0);ListIterator<Double> xit = x.listiterator();while (xit.hasNext()) { sum += (Double) xit.next();}


Multidimensional arrays

ArrayList<ArrayList> x = new ArrayList<ArrayList>()for(i=0;i<3;i++){

ArrayList<Int> y = new ArrayList<Int>()for( i=0; i<2; i++){

y.add(i);}x.add(y);

}

[ [ 1, 2 ] , [ 1, 2 ] ]


Matrix multiplication


Regression analysis


Regression analysisx = ((1, 6), (2, 5), (3, 7), (4, 10))y = α+ βx

6 = α+ β1

5 = α+ β2

7 = α+ β7

10 = α+ β4

S(α,β) = (6− (α+ β1))2+

(5− (α+ β2))2+

(7− (α+ β7))2+

(10− (α+ β4))2

We now minimize S, using partial derivatives for and using partial derivatives. This leads to the solution

α β

S(3.5, 1.4) = 1.12 + (−1)2 + (−0.7)2 + 0.92


Regression analysis


Use of “foreign” library or filesMany other Java sources are out there, for example - math libraries- plot libraries

We will look at the common math library by apache: http://commons.apache.org/math/index.html

Wikipedia definition of JAR files:A JAR file (or Java ARchive) aggregates many files into one.[1] Software developers generally use .jar files to distribute Java applications or libraries, in the form of classes and associated metadata and resources (text, images, etc.). JAR files build on the ZIP file format. Computer users can create or extract JAR files using the jar command that comes with a JDK. They can also use zip tools to do so; however, caution should be exercised as to the order of entries in the zip file headers as the manifest likely needs to be first.


http://commons.apache.org/math/index.html

http://commons.apache.org/math/index.html

http://en.wikipedia.org/wiki/Java_platform

http://en.wikipedia.org/wiki/Java_platform

http://en.wikipedia.org/wiki/Application_software

http://en.wikipedia.org/wiki/Application_software

http://en.wikipedia.org/wiki/Libraries

http://en.wikipedia.org/wiki/Libraries

http://en.wikipedia.org/wiki/Class_(file_format)

http://en.wikipedia.org/wiki/Class_(file_format)

http://en.wikipedia.org/wiki/Metadata

http://en.wikipedia.org/wiki/Metadata

http://en.wikipedia.org/wiki/ZIP_file_format




http://en.wikipedia.org/wiki/Java_Development_Kit

http://en.wikipedia.org/wiki/Java_Development_Kit

Installation into netbeans

If the distribution contains jar files for the classes, and the javadoc documentation, then the easiest way is to add the files to the Library by using the Tools menu in netbeans.


Regression analysis using commons-math


arrays, vectors , and matrices thursday 14th 2010

Documents